Python program that uses the Sieve of Eratosthenes method to compute prime numbers up to a specified number. Note: In mathematics, the sieve of Eratosthenes, (Ancient Greek: κόσκινον Ἐρατοσθένους, kóskinon Eratosthénous) one of a number of prime number sieves, is a simple, ancient algorithm for finding all prime numbers up to any given limit..
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Write a Python program that uses the Sieve of Eratosthenes method to compute prime numbers up to a specified number.
Note: In mathematics, the sieve of Eratosthenes, (Ancient Greek: κόσκινον Ἐρατοσθένους, kóskinon Eratosthénous) one of a number of prime number sieves, is a simple, ancient
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- In python, Problem Description:Sheldon and Leonard are physicists who are fixated on the BIG BANG theory. In order to exchange secret insights they have devised a code that encodes UPPERCASE words by shifting their letters forward. Shifting a letter by S positions means to go forward S letters in the alphabet. For example, shifting B by S = 3 positions gives E. However, sometimes this makes us go past Z, the last letter of the alphabet. Whenever this happens we wrap around, treating A as the letter that follows Z. For example, shifting Z by S = 2 positions gives B. Sheldon and Leonard’s code depends on a parameter K and also varies depending on the position of each letter in the word. For the letter at position P, they use the shift value of S = 3P + K. For example, here is how ZOOM is encoded when K = 3. The first letter Z has a shift valueof S = 3 × 1 + 3 = 6; it wraps around and becomes the letter F. The second letter, O, hasS = 3 × 2 + 3 = 9 and becomes X. The last two letters…In mathematics, a prime number is a natural number greater than 1 that is not a product of two smaller natural numbers, i.e. is it has only two factors 1 and itself. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways of writing it as a product, 1 × 5 or 5 × 1, involve 5 itself.Note that the prime number series is: 2, 3, 4, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, …a. Write a Java method named isPrime that takes a natural number as a parameter and returns the if the given number is prime or not using the following header: Public static boolean isPrime(int num) b. Write a Java class called PrimeNumbers that: o Reads from the user a natural value n (should be less than or equal 200). o Prints a list of the prime numbers from 2 to n and their number and values. o The program has to work EXACTLY as given in the following sample run.computePI(int n) – One remarkably simple formula for approximating the value of pi is the so-called Madhava–Leibniz series: pi/4 = 1 − 1/3+1/5 −1/7 +1/9 − ⋯ +/− 1/2n-1. Note that the result of the series is a quarter of pi. The accuracy of the approximation is dependent on the value of n. This method takes an int parameter n and calculates the value of pi, rather than pi/4. Pay attention to the sign (positive or negative) of each term. public double computePI(int n) { // TODO: implement this method return -1; //replace this statement with your own return; }
- In mathematics, a prime number is a natural number greater than 1 that is not a product of two smaller natural numbers, i.e. is it has only two factors 1 and itself. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways of writing it as a product, 1 × 5 or 5 x 1, involve 5 itself. Note that the prime number series is: 2, 3, 4, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, .. a. Write a Java method named isPrime that takes a natural number as a parameter and returns the if the given number is prime or not using the following header: Public static boolean isPrime (int num) b. Write a Java class called PrimeNumbers that: Reads from the user a natural value n (should be less than or equal 200). Prints a list of the prime numbers from 2 to n and their number and values. The program has to work EXACTLY as given in the following sample run. Hints: You should create a single dimension array to store the prime…Determine whether a string is a palindromeA palindrome is a string of characters that reads the same from right to left as it does from left to right, regardless of punctuation and spaces.The specifications for this assignment are: •Write and test a non-recursive solution in Java that determines whether a string is a palindrome •Your program should consist of at least two methods: (1) the main method (2) the method which performs the task of determining whether the specified string is a palindrome. You should name this method isPalindrome. You should name the class that contains your “main” method and the isPalindrome method FindPalindrome. •You must use a Stack and a Queue in your solution: Write your own Stack and Queue based on the Vector in the Java API and use those in your solution. You should name those classes StackVector and QueueVector respectively. You already have access to the relevant exception classes and interfaces for the above ADTs. •All of your belong to a Java…The Fibonacci algorithm is a famous mathematical function that allows us to create a sequence of numbers by adding together the two previous values. For example, we have the sequence:1, 1, 2, 3, 5, 8, 13, 21…Write your own recursive code to calculate the nth term in the sequence. You should accept a positive integer as an input, and output the nth term of the sequence.Once you have created your code, add comments describing how the code works, and the complexity of any code you have created.
- Parallel Lines python 3 Write a program to draw a set of linear lines with equation y = mx + b where m is the slope of the line and b is the y-intercept. Prompt user to enter the slope and y-intercept. Draw the line from x=-10 to x=10. Use numpy arange method to generate x values from -10 to 10 with step size of 0.1. For example., x = np.arange(-10, 10, 0.1) Use the plt.axis() function to set the range of x and y values from -10 to 10. Add xlabel with x-axis, ylabel with y-axis, and title Parallel Lines. After you have drawn the line, draw two lines that are parallel to the first line. Hint: Two lines are parallel if they have the same slope but different y-intercept. Draw two lines where the y-intercept value is one unit below the first line, and one unit above the first line. or example, if the first line y-intercept is 4, then draw lines with y-intercept of 3 and y-intercept of 5.A recursive function is a function defined in terms of itself via self-referential expressions. This means that the function will continue to call itself and repeat its behavior until some condition is met to return a result. Write a complete python program that includes a recursive python method, sumThem which accepts an argument, n, sums all the odd, or all the even, positive integers up to n*3, depending on whether n*3 is odd or even. The number should be entered by the user You should include in your answer a screenshot that shows the program and the output for the value n*3 where n must be equal your last ID digit. For example, if your ID is 201314151617, then 7 will be entered, and the calculations should be applied to 21. Expected Output Sample: Enter the number: 0 The sum of even numbers up to 0 will be: 0The greatest common divisor of two positive integers, A and B, is the largest number that can be evenly divided into both of them. Euclid's algorithm can be used to find the greatest common divisor (GCD) of two positive integers. You can use this algorithm in the following manner: 1. Compute the remainder of dividing the larger number by the smaller number. 2. Replace the larger number with the smaller number and the smaller number with the remainder. 3. Repeat this process until the smaller number is zero. The larger number at this point is the GCD of A and B. Write a program that lets the user enter two integers and then prints each step in the process of using the Euclidean algorithm to find their GCD. An example of the program input and output is shown below: Enter the smaller number: 5 Enter the larger number: 15 The greatest common divisor is 5
- Write factorial1 function in python 3.8 follow the directions provided below, don't need anything else as long as it meets all the requirements below. Function: factorial1 The function implements an iterative factorial. It takes an integer n as argument and returns n! The method needs to be computed interactively (not recursivelyUse the recursion to solve the following problems using Java Programming Language 1. Calculate the sum of an array of n integers. 2. Compute Powers, p(x,n)=xn 3. Revers an array of n integers 4. Calculate the length of string (number of characters) 5. Implement the tail recursion for problems 1 and 2. Please test the program by using 2 different input sets!mplement a Java program that applies the Newton-Raphson's method xn+1 = xn – f(xn) / f '(xn) to search the roots for this polynomial function ax6 – bx5 + cx4 – dx3+ ex2 – fx + g = 0. Fill out a, b, c, d, e, f, and g using the first 7 digits of your ID, respectively. For example, if ID is 4759284, the polynomial function would be 4x6 – 7x5 + 5x4 – 9x3+ 2x2 – 8x + 4 = 0. The program terminates when the difference between the new solution and the previous one is smaller than 0.00001 within 2000 iterations. Otherwise, it shows Not Found as the final solution.